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CHEM170 > Equations And Theory > Flashcards

Equations And Theory Flashcards

1
Q

What does phase velocity = ?

A

Phase velocity = frequency x wavelength

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2
Q

Convert radians to degrees

A

Radian = 2Pi / 360

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3
Q

What equation relates energy, h and frequency?

A

E = h v

(h = Planck’s constant)

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4
Q

How can E = hv also be written as?

A

E = h (c / lamda)

(As v = c / lamda)

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5
Q

What equation gives the energy of the rotational quantised levels?

A

E = BJ(J+1)

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6
Q

What is the equation of I - moment of inertia?

A

I = u r^2

Where r = bond length in m, and u = reduced mass

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7
Q

What are the selection rules for rotational spectroscopy?

A

For a pure rotational spectrum to be excited by microwave radiation, the molecule MUST possess a permanent dipole moment

E.g. HCl or CO

J (rotational quantum number) can only change by + or - 1.

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8
Q

How does vibrational spectroscopy differ to rotational spectroscopy?

A

Molecular vibration requires more energy than rotation

Pure vibration spectra occur in infrared region of EM spectrum (5000-100cm^-1)

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9
Q

What is the units of Joules and how can you remember this?

A

Kg m^2 s^-2
1 joule = 1 Nm

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10
Q

What is the units of Newtons and how can you remember this?

A

Kg m s^-2

F = m x a

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11
Q

How can molecules execute different types of vibrations?

A

By changing bond lengths or bond angles

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12
Q

What must happen to carry out vibrational spectroscopy?

A

Molecular vibration must give rise to a CHANGE in dipole moment

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13
Q

What’s the potential energy contribution in the PiB model?

A

0 - so there is only kinetic energy

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14
Q

What is the De Broglie formula?

A

Lambda = h / p

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15
Q

What expression can be used to describe the wavelengths that fit in the PiB model?

A

n(lambda / 2) = r

Where r = box length

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16
Q

How can the De Broglie formula be used to find the kinetic energy from momentum?

A

Rearrange de broglie for p

Rearrange PiB expression for lambda
- sub this into de broglie to get p = hn / 2r

Sub p = hn / 2r into kinetic energy of electron from momentum

Should get E = (h^2 n^2) / 8me r^2

n can only be a whole number, therefore E can only take certain specific quantised values. Hence th energy is quantised.

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17
Q

Why is the energy in PiB model quantised?

A

Because only certain, very specific wavelengths are allowed as n can only be an integer.

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18
Q

What is the lowest energy level in PiB model? Why is this?

A

E = 1 - as E1 is the energy of 1 half wavelength in the box, so E0 cannot exit as this would mean you have 0 half wavelengths in the box

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19
Q

Why is an absorption spectrum missing only special wavelengths? How does this relate to the Planck formula?

A

Because the electrons can only be in energies determined by the energy levels

Absorbing a particular wavelength = absorbing a particular energy - Planck formula

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20
Q

How do you find the number of vibrations a linear/non-linear molecule has?

A

Non-linear = 3N - 6 vibrations

Linear = 3N - 5 vibrations

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21
Q

How do you convert cm^-1 to m^-1?

A

X 100

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22
Q

How do you determine degeneracy?

A

2 J + 1 = degeneracy

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23
Q

What does degeneracy’s actually mean?

A

Degeneracy - in terms of QM - means the number of energy levels / sub-orbitals at a specific energy level.

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24
Q

What is the reduced mass equation?

A

u = ( m1m2 ) / ( m1 + m2 ) x 1.661x10^-27

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25
Q

Is the lowest energy in HO model 0? Why is this?

A

It’s not 0, its E0 = 1/2 h v

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26
Q

What is the name given to the energy present at absolute zero in the HO model?

A

Zero-point energy

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27
Q

What is the difference between the spacing of energy levels of HO and PiB models?

A

PiB has level spacing = (h^2 (2n+1) ) / 8me r^2

Harmonic oscillator has level spacing = hv

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28
Q

What does the harmonic oscillator model not allow? Why?

A

Molecule dissociation - when V > 0 molecule is not bound, HO shows any energy is possible after dissociation occurs - impossible

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29
Q

How can a full electron orbit about an atom be show in PiB model?

A

1 full wavelength - Wavefunction must be periodic

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30
Q

What is the equation for the moment of inertia for an electron orbiting a nucleus?

A

I = me r^2

(Where me = mass of electron)

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31
Q

What is the lowest possible energy of rotations? Why?

A

E = 0 - the electron is not rotating

This is because a straight line is the same at start and beginning - hence no zero-point energy.

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32
Q

When n = 0 what orbital does it produce and why? How many nodes?

A

S-orbital

No change of sign - no nodes

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33
Q

When n = 1 what orbital does it produce in 3D and why? How many nodes?

A

P-orbital

One sign change produced from single wavelength - also results in 1 node

34
Q

When n=2 what 3D orbital does it produce and why? How many nodes?

A

D-orbital

Two wavelengths produce 2 sign changes - results in 3 nodes

35
Q

What are l and m?

A

l is orbital angular momentum number - determines shape of orbital ( l = number of nodes )

ml is magnetic quantum number - determines the number of orbitals and their orientation ( ml is an interval from -l to +l )

36
Q

What is the quantum rotation number?

A

J

37
Q

How do atoms reach a favourable bond length?

A

Repulsive force pushing atoms apart if too close

An attractive potential - making atoms in bond move closer when too far apart

These forces result in a ‘well’ being formed of the lowest energy - hence most favourable

38
Q

What does thermodynamics state must be conserved?

A

Energy
Momentum
Angular momentum

(This is in an isolated system)

39
Q

What is V(r) a function of?

A

It is a function of the atoms position

This is only ever completely repulsive or attractive.

40
Q

What equation gives the potential energy of a spring?

A

V(r) = 1/2 k ( r - re )^2

Where re = equilibrium bond length
r = bond length

(The spring doesn’t exist but is a good model for the potential energy of the molecule)

41
Q

What’s the better model for potential energy PiB or HO?

A

Harmonic oscillator - HO potential has softened ends

42
Q

What is the importance of the Beer-Lambert law?

A

Intensity of spectral lines depends on it - and Boltzmann distributions

43
Q

What is the Beer-Lambert equation?

A

I = I0 10^-eCL

I is transmitted intensity
I0 is the incident intensity
L is the length of sample - longer = greater absorption
C is molar conc (moldm-3)
e is the molar absorption coefficient (mol-1dm3 cm-1)

44
Q

What does absorbance = ?

A

Abs = log I0 / I

45
Q

What does transmittance = ?

A

Trans = I0 / I

46
Q

What does E(bonding) = Alpha + Beta represent?

A

Alpha is the coulomb integral - the energy of one of the orbitals in the presence of both nuclei

Beta is the resonance integral - extra energy contribution when orbitals overlap, when electrons are shared between 2 atoms. This is the energy contribution from the mixing term.

47
Q

When atoms are far apart what does beta = ?

A

0 as the energy of the orbital only sees one atom.

48
Q

When atom A and B are close together, what happens to alpha?

A

Alpha becomes more negative as the energy increases due to the attraction of the wavefunction to both nuclei.

49
Q

What happens to beta when atoms A and B are close?

A

Beta is negative and decreases with r (bond length)

50
Q

Alpha and beta are both negative when close, what does this mean for anti-bonding?

A

a + B < a - B

a - B means energy is lost between the bond, so occupying this orbital makes bond weaker

51
Q

What is the energy difference between the bonding and anti-bonding levels?

A

2 Beta

(Beta is the resonance - mixing term - that gives us a covalent bond)

52
Q

Why is l = 0 for an s-orbital?

A

Because any rotation leaves the orbital unchanged

53
Q

How do you calculate bond order?

A

Bond order = 1/2 ( e- in bonding - e- in anti bonding )

54
Q

What is the general term for the number of nodes a wavefunction produces?

A

Nodes = n-1

55
Q

What does greater overlap result in?

A

Bigger molecular orbital

56
Q

Why can’t you combine a 1s orbital of an atom and a 2s orbital of another?

A

Atomic orbitals with very different energies do not combine well and form weak molecular orbitals - bonds.

57
Q

What do p-orbitals that are at right angles to the bond form?

A

Pi-orbitals

58
Q

Draw out sigma and pi bonding and anti-bonding orbitals using simple coin models

A
59
Q

What does paramagnetic mean?

A

Attracted to a magnetic field

60
Q

What is the order of molecular orbitals up to Nitrogen?

A

1∂ 2∂* 3∂ 4∂* 1pi 5∂ 2pi* 6∂*

61
Q

Why does the 1pi and 5∂ molecular orbitals swap between O2 and F2?

A

Because the effect of the 5∂ MO is much greater in smaller molecules, hence its energy drops as molecules increase in size.

62
Q

Draw a bonding and anti bonding s orbital in terms of PiB and a wavefunction

A
63
Q

What is the difference between bonding and anti-bonding ∂ orbitals in terms of nodes?

A

Bonding ∂ orbital has no nodes - wavefunction doesn’t change sign

Anti-bonding ∂ orbital has a node in centre of the bond - where wavefunction changes sign.

64
Q

What 3 options are there for triatomic molecules in terms of bonding and nodes?

A

Totally anti-bonding orbital - n = 3 with node separating all orbitals

No contribution from central atom - n = 2 with a node on top of central atom - non-bonding orbital

Totally bonding orbital - n = 1 - with no sign changes or nodes, every atom has a positive contribution to bonding.

The same applies for p orbitals

65
Q

What 3 vibrations can a molecule do?

A

Symmetric

Asymmetric

Bend

66
Q

What does 3 degrees of freedom mean for a molecule of N atoms?

A

It will have 3N degrees of freedom

Of this, 3 are translations, and 3 are rotations for non - linear

For linear molecules, there are 2 rotations

67
Q

What is the equation describing the oscillating behaviour of the bond length?

A

V = 1/2 k x^2

Where x = r - re (bond length - equilibrium bond length)

68
Q

The energy of the quantised vibrational levels are described by what equation?

A
69
Q

What equation gives the fundamental frequency v?

A

The greater the force constant k - the stronger the bond

70
Q

What frequency of photons do you need to cause a jump in energy levels in SHO model?

A

V (nu) - as levels are spaced evenly at hv throughout vibrational spec in SHO

71
Q

Why would you only see one ‘line’ in vibrational spectrum?

A

Because all ∆E = hv for ALL transitions - therefore only one ‘line’ present at frequency v (nu)

72
Q

What are the units of k - force constant?

A

Nm^-1

73
Q

What does/doesn’t change when the isotope of an atom is changed on vibrations?

A

Changing the isotope doesn’t change the strength of the bonds - k stays the same

Fundamental frequency changes because of reduced mass

74
Q

What is the benefit of using an Anharmonic Oscillator AHO?

A

It allows a molecule to dissociate

75
Q

How do you find the energy of bond dissociation?

A

The difference between V=0 (zero point energy) and the energy where the curve plateau’s - D0

76
Q

What happens to the bond length in an AHO when energy of system increases?

A

The equilibrium bond length increases until dissociation occurs

77
Q

What are the selection rules on of an AHO on vibrational spectra?

A

AHO allows ∆v to be + or - 1,2,3

More relaxed than SHO

78
Q

What are overtones in spectra?

A

Overtones are where you see additional bands at roughly 2v, 3v etc, with decreasing intensity.

Don’t occur exactly at 2v, 3v because vibrational energy levels converge as v increases due to anharmonicity

79
Q

How do you work out if a molecular vibration gives rise to a change?

A

Draw vibration at extremes of motion

Draw out individual bond dipoles

Draw out overall dipole

Compare overall dipole at 2 extremes, see if it changes

80
Q

What are skeletal vibrations?

A

Where most of the atoms in the molecule are induced (generally below 1500cm^1 and lie in ‘fingerprint’ region of spectrum

81
Q

How do characteristic group vibrations differ to skeletal vibrations?

A

Only small parts of the molecule are moving
- very defined functional groups only

Vibrational frequency observed is characteristic of that functional group, so gives direct clues of molecular structure

82
Q

What’s the equation for finding the energy of an electron in PiB?

A

CHEM170 (2 decks)

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